1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – SEPT/OCT. 2015

B.B.M. – V SEMESTER

M1 11 504: OPERATIONS RESEARCH

Duration: 3 Hours                                                                                         Max. Marks: 100

 

Section – A

1. Answer ALL the questions. Each carries 2 marks.                                         (2×10=20)

1)  Classify operation research models based on:

1. a) Time
2. b) Degree of certainity

 

2)  Mention any Four Features of Operation Research.

 

3) With reference to linear programming problems explain the following terms:

1. a) Infeasible solution
2. b) Redundant constraint

 

4) List any four areas of LPP application.

 

5) Introduce appropriate variables (slack, surplus or artificial) and convert the following    to equations

1. a) 3x + 5y < 15

b )4x + 3y >6

 

6)  Distinguish between PERT and CPM.

 

7)  A project manager has to manage various projects. For each project given below, you     are required to advise him whether to use PERT or CPM and briefly state the reason ?

 

1. Project K is yet to begin. The manager had recently successfully handled similar projects. He is able to break down the project into smaller modules and knows when he may comfortably finish each module.
2. Project M is new to the manager. He has never handled such a project he can break up the project into smaller modules, but even then, he is not sure of their exact times.

 

8)  How will you treat a Transportation problem with a Maximization objective?

 

9)  In case of an Unbalanced Assignment Matrix, what step is required to balance it?

 

 

10) Point out the errors in the network given below, going by the usual conventions while drawing a network to use CPM.

 

 

 

SECTION – B

1. II) Answer any FOUR questions. Each carries 5 marks.                                 (4×5=20)

 

11. Woods Product Ltd. currently produces two major products, tables and chairs. When sold, each chair yields a profit of `35 and table   `45.  An analysis of the production work sheets reveals the following manufacturing data:

Product	Man hrs. per unit	Machine hrs. per unit
Chair	5	0.8
Table	8	1.2
Time available during the year	800 Man hours	485 Machine hours

 

The company has a minimum demand for 50 chairs and a maximum demand for 25 tables during year 2013.  Construct an appropriate linear programme for maximizing the profit of Woods Product Ltd.

 

12. B. Sahni chartered accountant firm has four chartered accountants each of whom can be assigned any of the three audit assignments. Because of the varying work experience of the chartered accountants, the net surplus (professional fees minus expenses to be incurred by the CA firm) varies as under:

	Audit Assignments
Chartered Accountant	W	X	Y
A	65	78	83
B	85	52	59
C	83	56	69
D	49	80	85

 

You are required to find the maximum net surplus which can be obtained.

 

13. a) Solve the following transportation problem by
14. North west corner Rule (NWCR)
15. Least Cost Method (LCM)

D W	D1	D2	D3	D4	D5	Availability
W1	3	4	6	8	8	20
W2	2	10	0	5	8	30
W3	7	11	20	40	3	15
W4	1	0	9	14	16	13
Required	40	6	8	18	6	78

 

1. Is the cost of transportation reduced through LCM in comparison to the  NWCR,  if so to what extent?

 

14. Find the Dual of the following problem:

Maximize      Z = 30 x₁   +  20 x₂

Subject to constraints:  -x₁ – x₂ > -8

-6x₁ – 4x₂ < – 12

5x₁ + 8x₂ = 20

x₁, x₂ >0

 

15. What is meant by decision tree analysis? Explain the types of decision making environment?

 

16. The following table gives the activities in a construction project and the time duration of each activity:

Activity	Preceding activity	Normal time (days)
A	–	16
B	–	20
C	A	8
D	A	10
E	B,C	6
F	D,E	12

Required :

1. Draw the activity network of the project.
2. Find the critical path.

 

Section- C

1. II) Answer any THREE questions. Each carries 15 marks.                                 (3×15=45)

 

17. Solve the following LPP by using the Big – M method

Max Z=10x+12y

Subject to constraints

x + y=5

x > 2

y < 4

where    x, y >0

18. A car hire company has one car at each of the five depots M,N, O, P & Q. A customer in each of the five towns A,B,C,D,&E, requires a car. the distance (in miles)between the depots (origins) and the towns (destinations) where the customers are, are given in the following distance matrix.

		M	N	O	P	Q
Person	A	160	130	175	190	200
	B	135	120	130	160	175
	C	140	110	155	170	185
	D	50	50	80	80	110
	E	55	35	70	80	105

How should the cars be assigned to the customers so as to minimize the distance travelled. Solve the above Assignment problem by using  the Hungarian Method.

 

19. A) A Small project is composed of seven activities, whose times estimates (in days) are listed below. Activities are identified by their beginning (i) and ending (j) node numbers.

Activity (i-j)	1-2	1-3	1-4	2-5	3-5	4-6	5-6
Duration to	2	2	4	2	4	4	6
Duration  tm	2	8	4	2	10	10	12
Duration tp	14	14	16	2	28	16	30

1. Draw the project network
2. Find the Expected Duration and Variance for each activity. What is the expected project length?
3. If the project due date is 38 days, what is the probability of meeting the due date?

 

19.B) Given that operation research represents an integrated framework to help make decisions, it is important to have a clear understanding of this framework so that it can be applied to a generic problem.  In light of the above statement examine the methodology / steps involved in solving an Operation Research problem.

(10+5)

20. The following linear program is presented to you:

Objective  :Maximize Z=30X +45Y Subjective to :  (i)2X+3Y, < 1,440 (ii) 9X+12Y > 2,160 (iii) 3x + 4y > 1080 (iv) x,y >0.

Required: Draw the Graph taking quantities of x and y in the respective axes in steps of 60 units (scale 1 cm = 60units) and solve the following LPP Determine the optimality and offer your comments on the solution and the constraints

21) The activities in respect of a maintenance project are as below:

Activity	1-2	1-3	1-4	2-5	3-6	3-7	4-7	5-8	6-8	7-9	8-9
Months	2	2	1	4	5	8	3	1	4	5	3

1. Draw the project network.
2. Find the Critical Path and Duration of the project.
3. Perform the forward and backward pass computations and derive the EST, EFT, LST and LFT for each event/activity.
4. Determine Total Float, Free Float and Independent Float.

SECTION –D

1. IV) Case Study – Compulsory question.          (1×15=15)
2. A company has four factories F1, F2, F3 & F4 manufacturing the same product. Production and raw material cost differ from factory to factory and given in the following table.  The transportation cost from the factories to the sales depots S1, S2 & S3 are also given.  The costs, total requirement  at each depot and also the product capacity at each factory are also stated below.

	F1	F2	F3	F4	Requirement
S1	19	30	50	10	7
S2	70	30	40	60	9
S3	40	8	70	20	18
Capacity	5	8	7	14	34

1. Obtain an IBFS to minimize the costs of the following transportation problem by VAM:
2. Test the optimality of the solution thus obtained using the MODI method.
3. Is the solution degenerate?
4. If need be optimize the solution.

 

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